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Heat a medium saucepan over medium-high heat.
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Add 1 tablespoon of the butter, then the celery and onions.
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Sauté until the vegetables are golden, about 5 minutes.
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Remove from the pan and reserve.
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Add the potatoes and just enough water to cover to the pan.
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Season generously with salt.
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Bring the water to a boil, cover, reduce heat to medium-low and cook until potatoes are tender.
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This should take about 15 minutes.
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Drain the potatoes and return the pan to a medium heat.
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Stir in the cooked vegetables, 3 tablespoons of butter and milk.
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Mash lightly with a masher or fork.
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Add more salt, pepper and taste for seasoning.
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Serve immediately or keep warm over low heat with the lid slightly opened.